No because the difficulty only changes every 2,016 blocks. If all miners shut down, nobody would find enough blocks until the next difficulty readjustment.

So we'd be fine if the miners shut down after the 2,015th block after the previous difficulty adjustment?

No because the next block would have a new difficulty. But that difficulty would be calculated on the timestamps of the previous 2,016 blocks (if they took more than two weeks, difficulty goes down, otherwise it goes up) so the difficulty would still be normal and require roughly as many miners as we have now to keep it going.